Motion of liquid and stabilising particles in individual liquid aluminium alloy films

To give a first overview, particles permanently in motion (type 1 as defined in the introduction) in an AlSi9Mg0.6/SiC/20p film are highlighted by temporally colour-coded particle trajectories (Fig. 2). Particles that remained fixed throughout the experiment (type 2) were removed. Background correction, integration over the minimum intensity value and colouration were performed to plot the path of the particles. Each colour stands for the time at which a single frame was taken. This simple visualization technique already makes the complexity of particle movements evident. Both downward and horizontal particle motions can be observed, which are caused by gravity forces and capillary suction into the Plateau border situated on the right edge of the images, respectively. To further analyse different aspects of liquid dynamics, several quantifying analyses were performed by image processing. Interactions of different particle types are summarised in “Direction change of particle motion” section.

In Fig. 3a, the total area of moving particles in the film shown in Fig. 2 is given. The threshold value of a moving cluster or particle is set to 1.2 pixels (3.24 μm). At the beginning of the analysis, most of the moving particles are present in the FOV but consecutively leave it as time elapses, i.e. they are of type 1. This is reasonable considering the film pulling procedure: Initially, films are thick and full of particles and oxidation is at a low level and therefore particle retention is weak.

Classifying and counting the number of particles or particle clusters with respect to their size (large or small) yields Fig. 3b, c. Small clusters (here ≤ 3645 µm²) represent the major category of moving clusters, compare scaling of Fig. 3b, c. A similar decay for particle numbers is observed as for the global area given in Fig. 3a. After around 25 s almost no big cluster is moving any more. This means that particles are either collected at the bottom (outside the FOV) or stick to the oxide layer (within the FOV). The former particles are of type 1, and the latter of type 3. Big clusters cannot flow anymore after a certain time due to the film thickness reduction that restrains big objects immersed in the fluid film.

The average velocity of clusters as well as their horizontal (\(x\)) and vertical (\(y\)) components are analysed and shown in Fig. 4. The measurements show that clusters decelerate in the vertical but accelerate in the horizontal direction within the first 5 s (Fig. 4b, c), decelerating slightly on average (Fig. 4a). Particles move to the right here due to the suction of the Plateau border situated at the right side of the image. The downward movement follows gravity forces. As the SiC particles flow in the melt, we can assume that they move with the velocity of the liquid.

Right after film pulling the acceleration of particles/clusters is driven mainly by gravitational forces, therefore a fast downward but only moderate movement to the right. Later, particles/clusters are pushed out of the film due to increasingly radially acting (in our FOV horizontal) capillary forces and slow down downward induced by film thinning (see Fig. 5b). This situation is similar to that in aqueous films [16].

Based on Hagen-Poiseuille flow between two immobile surfaces, the time-dependent loss of liquid volume V in a vertically arranged film can be written as [7, 17, 18]where x(t) is the time-dependent film thickness, ρ is the liquid density (2.42 g cm⁻³ for AlSi9 at 700 °C [19]), l is the lamella width, µ melt viscosity (3.3 mPa s for AlSi9/SiC/20p at 700 °C [20]), and g = 9.81 m s⁻² gravity acceleration. The liquid volume in a simplified lamella is [7, 18]where h and l are the lamella height and width, respectively, corresponding here to the dimension of the selected FOV of 3.5 × 3.5 mm. Assuming l and h as constant, the time dependence of the volume is then

Substituting (2) and (3) into Eq. (1), integration of Eq. (1) and solving it for x(t) results in an expression for the time-dependent film thickness: [17, 18]where x₀ = 4 µm is the starting lamella thickness during film pulling after t = −2 s [7]. Furthermore, and assuming that no liquid flows out of the FOV horizontally, what is approximately the case at t = 0 s (see Fig. 4b), the vertical velocity of the liquid can be expressed asThis simple model results in an extremely fast film thinning with the given parameters (see Fig. 5a) [7]. Accordingly, the film should have already thinned down to x = 37 µm at t = 0 s (2 s after film pulling, when the measurement starts). However, the reported minimum film thickness is x_min ≈ 50 µm [5, 21, 22] and the measured film thickness of the solidified lamella in this work after x(> 30 s) ≈ 300 µm as shown in Fig. 1. A possible interpretation of this result is that the model underestimates the viscosity of the liquid in the film, especially when the film thickness approached the size of the largest clusters. Applying the increased effective viscosity reported previously [23], namely µ = 150 mPa s for AlSi9/SiC/20p at 700 °C, the film thickness at t = 0 s changes to x(0 s) = 250 µm. The time at which the horizontal velocity is zero is t = −0.5 s as derived by extrapolating Fig. 4b. Evaluating Fig. 5a, we then obtain x(−0.5 s) = 300 µm for the initial thickness of the film.

In our experiment, the vertical velocity, and therefore the film thickness, seem to remain constant during the whole measurement time due to the stabilising effect of the SiC particle clusters preventing the film from further thinning. This is because there is sufficient liquid stored in the Plateau border that feeds the volume of the much thinner film and maintains an equilibrium during the measurement. The vertical velocity of the particle clusters corresponds to dy/dt = 117 µm s⁻¹ according to Eq. (5), see Fig. 5b, which is quite close to the measured mean velocity of 134 ± 41 µm s⁻¹ given in Fig. 4c.

In Fig. 6, the velocity of particle clusters is plotted separately for three distinct particle size categories. The velocity of the largest clusters (> 3645 µm²) shows large statistical scatter due to their low number. Their average velocity is ~ 400 µm s⁻¹ at the beginning and remains higher (~ 351 ± 63 µm s⁻¹) than the nearly constant velocities of medium-sized (264 ± 9 µm s⁻¹) and small clusters (233.79 ± 12 µm s⁻¹) in the period 0–20 s. A notable deceleration of large clusters down to 159 ± 62 µm s⁻¹ takes place from 20–28 s, 30% to 40% lower than medium-sized and small particles. This effect can be explained by particle jamming caused by progressive particle attachment to surface oxide layers. Assuming spherical clusters, the diameter of the largest cluster (> 3645 µm²) is D > 64 µm, hindering the film to further thinning. This is in accordance with the observed minimal film thickness of x_min ≈ 50 µm [4, 20, 21] in metal foams. Thus, big clusters with diameters close to the film thickness might be decelerated by the parabolic velocity profile over the film thickness as postulated by Hagen-Poiseuille. This effect may be caused by friction with the surface oxide skin or with other clusters of type 2, while smaller clusters continue flowing without such hindrance through regions closer to the centre of the film. The presence of an immobilised surface skin is plausible as the gas–liquid interface oxidises immediately and forms a solid oxide skin [7, 24‐26].

The directions of particle motions and how they change over time are specified in Fig. 7. Both the number of particles per angle (Fig. 7a) and the total area of all particles moving in an angle interval (Fig. 7b) are given. In accordance with Fig. 3, the majority of the particles (hence in red) initially move at an angle of 180°, which is defined as the downward direction, i.e. they are driven by gravity. After a holding time > 7 s, however, Fig. 7a, b shows that some clusters undergo a gradual change in direction from vertical towards a flow to the right (90°) and into the Plateau border, compare Fig. 2. An increased number of clusters is found to move at angles around 60° at specific times (upper graph), which implies that mainly smaller clusters (as most clearly seen in the video, Online Resource (1)) have an upward velocity component, i.e. opposing gravity, see also Fig. 2. In this particular case, capillary suction induced by film thinning is stronger than gravity-induced drainage. In two special time intervals, 6.2–7.6 s and 15.4–16.6 s, clusters are found to move straight upwards, but this is caused by the capture of particles by small bubbles, which appeared during stirring or film pulling. The origin of these bubbles can be gas trapped in the slag or in porous oxide skins, which can form already by 1500 ppm of O₂ [8].

An experiment on an AlSi9Mg0.6/SiC/20p film drawn in air (21% O₂) is represented by Fig. 8 (see videos in Online Resources 1 and 2). A high oxygen content is known to influence particle flow and especially sticking [7], but it is not the purpose of this paper to study this in detail. A similar change of direction due to capillary suction as in the previous examples is found. This force caused by film curvature and surface tension leads to film thinning. Initially (0–4 s), particles and clusters follow curvy (vertical as well as horizontal) paths from the top of the film out of the FOV. After 6 s, they are found to tend towards the Plateau border. In region 2 of Fig. 8b, a transition from vertical to horizontal flow into the Plateau border can be seen, which eventually predominates in (region 3), while in the Plateau border vertical flow caused by gravity continues (region 1). In region 4, capillary suction is found to be strong enough to force particles to flow to the left into the Plateau border, but also upwards against gravity. Furthermore, it is found that all particles flowing into the Plateau border (velocity ~ 100 µm/s) change direction and accelerate again in region 1 (to ~ 300 µm/s). A theoretical approach was developed by Gergely and Clyne [4]. They described drainage dynamics in metal foams and found that high foam porosity, small bubbles and a vertical gradient in capillary pressure facilitate gravity-driven melt flow.

What happens if the main exit path of particles out of a Plateau border is blocked is shown in Fig. 9. Here, particles also flow mainly downward in the first seconds but also turbulently before leaving the film or getting blocked by already fixed clusters (white noise spots). This behaviour is found to be enhanced in films pulled under 21% O₂ compared to films prepared in 1500 ppm oxygen.

By considering only raw image sequences as in Ref. [7], it was found that some initially moving particles or clusters suddenly stop and do not move any further (called type 3). The reason was found in interactions with the growing oxide layer on the film surfaces [7].

In the current paper, we find that such clusters do not necessarily remain trapped indefinitely, but are able to detach and attach again (DA process). To visualise this effect, Fig. 10 shows the results of several image processing steps such as background correction and integration over 0.1 s of all pixels above a given minimum intensity threshold. They emphasise particles in motion (type 1 and 3 partially). To highlight only particles of type 3 (green), particles that remain fixed throughout the experiment (type 2) are eliminated by subtraction of the average of the first 1 s, whereas particles of type 1 are still visible (grey) by blurring particle trajectories obtained by integration. In Fig. 10, fast moving particles (type 1 and 3 before attachment) are marked in dark grey, whereas particles which attach and might get released again (type 3 only) are marked in green. Here it was found that this phenomenon is linked closely to the liquid dynamics already presented in previous figures. Thus, each column in Fig. 10 represents one specific event of Figs. 3, 4, 5, 6, 7 (yellow bars). The first event—after 5.2 s—shows, that an already fixed cluster (type 3) undergoes a DA process, although the motion is small and difficult to observe. Considering Fig. 4, it can also be seen that the flow of this cluster is rather wiggling than directed straight downwards. After 6.2 s, a particle cluster entering the FOV from the bottom rises and attaches to an already fixed cluster (Fig. 10b). This fast upwards flow is driven by the buoyancy of the attached gas bubble and can also be found in Fig. 7. Although the flow is upwards, those particle-bubble-clusters can also be fixed (7.6–7.7 s). The event in the third column (after 8.5 s, Fig. 10c) is similar to the first, where the particle cluster detaches but leaves the FOV and does not attach again. Furthermore, this cluster is mostly an agglomeration of several small particles as it can be seen in comparison with Fig. 3. Its slight trend to the Plateau border is caused by capillary suction. After 12.3 s and 13.1 s (Fig. 10d), two further DA processes of the same cluster as in Fig. 10a are shown. The special behaviour between 12.3−12.6 s is that particles are wiggling and only moving slightly downward, whereas between 13.1 and 13.7 s (Fig. 10e) the DA process is more dominating, so that three neighbouring clusters are affected at the same time. In the last column, Fig. 10f, the global change is even more conspicuous: after 15.1 s seven already fixed clusters detach, whereas six flow down and one upwards. The reason for the upwards flow is the same as in the second column and caused by attached gas bubbles. Triggering of this collective movement seems to be spontaneous, as the global velocity (Fig. 4) or direction distribution (Fig. 7) is constant for time periods < 15.1 s. One suggestion is that the surface oxide layer ruptures perpendicular to the pulling direction as the curvature, respectively surface, of the film evolves during thinning [10]. Fixed particles can move together with the oxide layer until the new oxide layer forms and the film surface rests again. This is reasonable as Al is known to oxidise immediately [27]. This effect should be even larger in a film that is part of an expanding metal foam and that is stretched continuously unlike the more static film studied here.